This function provides a general framework for using the marginal treatment effect (MTE) to extrapolate. The model is the same binary treatment instrumental variable (IV) model considered by Imbens and Angrist (1994) (10.2307/2951620) and Heckman and Vytlacil (2005) (10.1111/j.1468-0262.2005.00594.x). The framework on which this function is based was developed by Mogstad, Santos and Torgovitsky (2018) (10.3982/ECTA15463). See also the recent survey paper on extrapolation in IV models by Mogstad and Torgovitsky (2018) (10.1146/annurev-economics-101617-041813). A detailed description of the module and its features can be found in Shea and Torgovitsky (2021).
ivmte(
data,
target,
late.from,
late.to,
late.X,
genlate.lb,
genlate.ub,
target.weight0 = NULL,
target.weight1 = NULL,
target.knots0 = NULL,
target.knots1 = NULL,
m0,
m1,
uname = u,
m1.ub,
m0.ub,
m1.lb,
m0.lb,
mte.ub,
mte.lb,
m0.dec,
m0.inc,
m1.dec,
m1.inc,
mte.dec,
mte.inc,
equal.coef,
ivlike,
components,
subset,
propensity,
link = "logit",
treat,
outcome,
solver,
solver.options,
solver.presolve,
solver.options.criterion,
solver.options.bounds,
lpsolver,
lpsolver.options,
lpsolver.presolve,
lpsolver.options.criterion,
lpsolver.options.bounds,
criterion.tol = 1e-04,
initgrid.nx = 20,
initgrid.nu = 20,
audit.nx = 2500,
audit.nu = 25,
audit.add = 100,
audit.max = 25,
audit.tol,
rescale,
point,
point.eyeweight = FALSE,
bootstraps = 0,
bootstraps.m,
bootstraps.replace = TRUE,
levels = c(0.99, 0.95, 0.9),
ci.type = "backward",
specification.test = TRUE,
noisy = FALSE,
smallreturnlist = FALSE,
debug = FALSE
)data.frame or data.table used to estimate
the treatment effects.
character, target parameter to be estimated. The
function allows for ATE ('ate'), ATT ('att'), ATU
('atu'), LATE ('late'), and generalized LATE
('genlate').
a named vector or a list declaring the baseline values of Z used to define the LATE. The name associated with each value should be the name of the corresponding variable.
a named vector or a list declaring the comparison set of values of Z used to define the LATE. The name associated with each value should be the name of the corresponding variable.
a named vector or a list declaring the values to condition on. The name associated with each value should be the name of the corresponding variable.
lower bound value of unobservable u for
estimating the generalized LATE.
upper bound value of unobservable u for
estimating the generalized LATE.
user-defined weight function for the control
group defining the target parameter. A list of functions can be
submitted if the weighting function is in fact a spline. The
arguments of the function should be variable names in
data. If the weight is constant across all observations,
then the user can instead submit the value of the weight
instead of a function.
user-defined weight function for the treated
group defining the target parameter. See target.weight0
for details.
user-defined set of functions defining the
knots associated with spline weights for the control group. The
arguments of the function should consist only of variable names
in data. If the knots are constant across all
observations, then the user can instead submit the vector of
knots instead of a function.
user-defined set of functions defining the
knots associated with spline weights for the treated group. See
target.knots0 for details.
one-sided formula for the marginal treatment response
function for the control group. Splines may also be
incorporated using the expression uSpline, e.g.
uSpline(degree = 2, knots = c(0.4, 0.8), intercept =
TRUE). The intercept argument may be omitted, and is
set to TRUE by default.
one-sided formula for the marginal treatment response
function for the treated group. See m0 for details.
variable name for the unobservable used in declaring the MTRs. The name can be provided with or without quotation marks.
numeric value for upper bound on MTR for the treated group. By default, this will be set to the largest value of the observed outcome in the estimation sample.
numeric value for upper bound on MTR for the control group. By default, this will be set to the largest value of the observed outcome in the estimation sample.
numeric value for lower bound on MTR for the treated group. By default, this will be set to the smallest value of the observed outcome in the estimation sample.
numeric value for lower bound on MTR for the control group. By default, this will be set to the smallest value of the observed outcome in the estimation sample.
numeric value for upper bound on treatment effect parameter of interest.
numeric value for lower bound on treatment effect parameter of interest.
logical, set to FALSE by default. Set equal to
TRUE if the MTR for the control group should be weakly
monotone decreasing.
logical, set to FALSE by default. Set equal to
TRUE if the MTR for the control group should be weakly
monotone increasing.
logical, set to FALSE by default. Set equal to
TRUE if the MTR for the treated group should be weakly
monotone decreasing.
logical, set to FALSE by default. Set equal to
TRUE if the MTR for the treated group should be weakly
monotone increasing.
logical, set to FALSE by default. Set equal
to TRUE if the MTE should be weakly monotone decreasing.
logical, set to FALSE by default. Set equal
to TRUE if the MTE should be weakly monotone increasing.
one-sided formula to indicate which terms in
m0 and m1 should be constrained to have the same
coefficients. These terms therefore have no effect on the MTE.
formula or vector of formulas specifying the
regressions for the IV-like estimands. Which coefficients to
use to define the constraints determining the treatment effect
bounds (alternatively, the moments determining the treatment
effect point estimate) can be selected in the argument
components. If no argument is passed, then a linear
regression will be performed to estimate the MTR coefficients.
a list of vectors of the terms in the regression
specifications to include in the set of IV-like estimands. No
terms should be in quotes. To select the intercept term,
include the name intercept. If the factorized
counterpart of a variable is included in the IV-like
specifications, e.g. factor(x) where x = 1, 2, 3,
the user can select the coefficients for specific factors by
declaring the components factor(x)-1, factor(x)-2,
factor(x)-3. See l on how to input the
argument. If no components for a IV specification are given,
then all coefficients from that IV specification will be used
to define constraints in the partially identified case, or to
define moments in the point identified case.
a single subset condition or list of subset
conditions corresponding to each regression specified in
ivlike. The input must be logical. See l
on how to input the argument. If the user wishes to select
specific rows, construct a binary variable in the data set, and
set the condition to use only those observations for which the
binary variable is 1, e.g. the binary variable is use,
and the subset condition is use == 1.
formula or variable name corresponding to
propensity to take up treatment. If a formula is declared, then
the function estimates the propensity score according to the
formula and link specified in link. If a variable name
is declared, then the corresponding column in the data is taken
as the vector of propensity scores. A variable name can be
passed either as a string (e.g propensity = 'p'), a
variable (e.g. propensity = p), or a one-sided formula
(e.g. propensity = ~p).
character, name of link function to estimate propensity
score. Can be chosen from 'linear', 'probit', or
'logit'. Default is set to 'logit'. The link
should be provided with quoation marks.
variable name for treatment indicator. The name can be provided with or without quotation marks.
variable name for outcome variable. The name can be provided with or without quotation marks.
character, name of the programming package in R used
to obtain the bounds on the treatment effect. The function
supports 'gurobi', 'cplexapi', rmosek,
'lpsolveapi'. The name of the solver should be provided
with quotation marks.
list, each item of the list should correspond to an option specific to the solver selected.
boolean, default set to TRUE. Set
this parameter to FALSE if presolve should be turned off
for the LP/QCQP problems.
list, each item of the list should correspond to an option specific to the solver selected. These options are specific for finding the minimum criterion.
list, each item of the list should correspond to an option specific to the solver selected. These options are specific for finding the bounds.
character, deprecated argument for lpsolver.
list, deprecated argument for
solver.options.
boolean, deprecated argument for
solver.presolve.
list, deprecated argument for
solver.options.criterion.
list, deprecated argument for
solver.options.bounds.
tolerance for the criterion function, and is
set to 1e-4 by default. The criterion measures how well the
IV-like moments/conditional means are matched using the
l1-norm. Statistical noise may prohibit the theoretical LP/QCQP
problem from being feasible. That is, there may not exist a set
of MTR coefficients that are able to match all the specified
moments. The function thus first estimates the minimum
criterion, which is reported in the output under the name
'minimum criterion', with a criterion of 0 meaning that all
moments were able to be matched. The function then relaxes the
constraints by tolerating a criterion up to minimum
criterion * (1 + criterion.tol). Set criterion.tol to a
value greater than 0 to allow for more conservative bounds.
integer determining the number of points of the covariates used to form the initial constraint grid for imposing shape restrictions on the MTRs.
integer determining the number of points in the
open interval (0, 1) drawn from a Halton sequence. The end
points 0 and 1 are additionally included. These points are
always a subset of the points defining the audit grid (see
audit.nu). These points are used to form the initial
constraint grid for imposing shape restrictions on the u
components of the MTRs.
integer determining the number of points on the covariates space to audit in each iteration of the audit procedure.
integer determining the number of points in the
open interval (0, 1) drawn from a Halton sequence. The end
points 0 and 1 are additionally included. These points are used
to audit whether the shape restrictions on the u
components of the MTRs are satisfied. The initial grid used to
impose the shape constraints in the LP/QCQP problem are
constructed from a subset of these points.
maximum number of points to add to the initial
constraint grid for imposing each kind of shape constraint. For
example, if there are 5 different kinds of shape constraints,
there can be at most audit.add * 5 additional points
added to the constraint grid.
maximum number of iterations in the audit procedure.
feasibility tolerance when performing the
audit. By default to set to be 1e-06, which is equal to the
default feasibility tolerances of Gurobi (solver =
"gurobi"), CPLEX (solver = "cplexapi"), and Rmosek
(solver = "rmosek"). This parameter should only be
changed if the feasibility tolerance of the solver is changed,
or if numerical issues result in discrepancies between the
solver's feasibility check and the audit.
boolean, set to TRUE by default. This
rescalels the MTR components to improve stability in the
LP/QCQP optimization.
boolean. Set to TRUE if it is believed that the
treatment effects are point identified. If set to TRUE
and IV-like formulas are passed, then a two-step GMM procedure
is implemented to estimate the treatment effects. Shape
constraints on the MTRs will be ignored under point
identification. If set to TRUE and the regression-based
criteria is used instead, then OLS will be used to estimate the
MTR coefficients used to estimate the treatment effect. If not
declared, then the function will determine whether or not the
target parameter is point identified.
boolean, default set to FALSE. Set to
TRUE if the GMM point estimate should use the identity
weighting matrix (i.e. one-step GMM).
integer, default set to 0. This determines the number of bootstraps used to perform statistical inference.
integer, default set to size of data
set. Determines the size of the subsample drawn from the
original data set when performing inference via the
bootstrap. This option applies only to the case of constructing
confidence intervals for treatment effect bounds, i.e. it does
not apply when point = TRUE.
boolean, default set to TRUE. This
determines whether the resampling procedure used for inference
will sample with replacement.
vector of real numbers between 0 and 1. Values correspond to the level of the confidence intervals constructed via bootstrap.
character, default set to 'both'. Set to
'forward' to construct the forward confidence interval
for the treatment effect bound. Set to 'backward' to
construct the backward confidence interval for the treatment
effect bound. Set to 'both' to construct both types of
confidence intervals.
boolean, default set to
TRUE. Function performs a specification test for the
partially identified case when bootstraps > 0.
boolean, default set to TRUE. If TRUE,
then messages are provided throughout the estimation
procedure. Set to FALSE to suppress all messages,
e.g. when performing the bootstrap.
boolean, default set to FALSE. Set to
TRUE to exclude large intermediary components
(i.e. propensity score model, LP/QCQP model, bootstrap
iterations) from being included in the return list.
boolean, indicates whether or not the function should
provide output when obtaining bounds. The option is only
applied when solver = 'gurobi' or solver =
'rmosek'. The output provided is the same as what the Gurobi
API would send to the console.
Returns a list of results from throughout the estimation procedure. This includes all IV-like estimands; the propensity score model; bounds on the treatment effect; the estimated expectations of each term in the MTRs; the components and results of the LP/QCQP problem.
When the function is used to estimate bounds, and statistical inference is not performed, the function returns the following objects.
the number of audits required until there were no more violations; or the number of audits performed before the audit procedure was terminated.
the minimum criterion.
a list containing the points used to define the audit grid, as well as a table of points where the shape constraints were violated.
a vector with the estimated lower and upper bounds of the target treatment effect.
a list containing all the model specifications and call options generating the results.
a list containing the estimate of the weighted means
for each component in the MTRs. The weights are determined by the
target parameter declared in target, or the weights defined
by target.weight1, target.knots1,
target.weight0, target.knots0.
a list containing the coefficients on the treated and control group MTRs.
a list containing the target weights used to
estimate gstar.
a list containing the LP/QCQP model, and the full output from solving the problem.
the solver used in estimation.
the number of elements in the S-set used to generate achieve (partial) identification.
the propensity score model. If a variable is fed
to the propensity argument when calling ivmte, then
the returned object is a list containing the name of variable given
by the user, and the values of that variable used in estimation.
a list of all the coefficient estimates and weights corresponding to each element in the S-set.
a list including the specifications of each spline declared in each MTR.
a vector of character strings logging the output of the estimation procedure.
If bootstraps is greater than 0, then statistical inference
will be performed and the output will additionally contain the
following objects.
the number of bootstraps.
the number of bootstraps that failed (e.g. due to collinearity) and had to be repeated.
the estimates of the bounds from every bootstrap draw.
forward and/or backward confidence intervals for
the bound estimates at the levels specified in levels.
bootstrap standard errors on the lower and upper bound estimates.
p-value for the estimated bounds. p-values are constructed by finding the level at which the confidence interval no longer contains 0.
confidence interval for coefficient estimates of the propensity score model.
standard errors for the coefficient estimates of the propensity score model.
p-value from a specification test. The specification test is only performed if the minimum criterion is not 0.
If point = TRUE and bootstraps = 0, then point
estimation is performed using two-step GMM. The output will contain
the following objects.
test statistic and results from the asymptotic J-test.
a vector. Each element is the GMM criterion for each moment condition used in estimation.
coefficient estimates for the MTRs.
point estimate of the treatment effect.
indexes for the moment conditions (i.e. elements in the S set) that were linearly independent and could be dropped.
If point = TRUE and bootstraps is not 0, then
point estimation is performed using two-step GMM, and additional
statistical inference is performed using the bootstrap samples.
The output will contain the following additional objects.
the number of bootstraps.
the number of bootstraps that failed (e.g. due to collinearity) and had to be repeated.
test statistic and result from the J-test performed using the bootstrap samples.
J-test statistic from each bootstrap.
coefficient estimates for the MTRs from each bootstrap sample. These are used to construct the confidence intervals and standard errors for the MTR coefficients.
confidence intervals for each MTR coefficient.
standard errors for each MTR coefficient estimate.
p-value for the treatment effect point estimate estimated using the bootstrap.
treatment effect point estimate from each bootstrap sample. These are used to construct the confidence interval, standard error, and p-value for the treatment effect.
confidence interval for the treatment effect.
standard error for the treatment effect estimate.
confidence interval for the coefficients in the propensity score model, constructed using the bootstrap.
standard errors for the coefficient estimates of the propensity score model.
# NOT RUN {
dtm <- ivmte:::gendistMosquito()
ivlikespecs <- c(ey ~ d | z,
ey ~ d | factor(z),
ey ~ d,
ey ~ d | factor(z))
jvec <- l(d, d, d, d)
svec <- l(, , , z %in% c(2, 4))
ivmte(ivlike = ivlikespecs,
data = dtm,
components = jvec,
propensity = d ~ z,
subset = svec,
m0 = ~ u + I(u ^ 2),
m1 = ~ u + I(u ^ 2),
uname = u,
target = "att",
m0.dec = TRUE,
m1.dec = TRUE,
bootstraps = 0,
solver = "lpSolveAPI")
# }
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